Functions of genus zero for which the fast escaping set has Hausdorff dimension two


Sixsmith, DJ ORCID: 0000-0002-3543-6969 (2013) Functions of genus zero for which the fast escaping set has Hausdorff dimension two. Proc. Amer. Math. Soc., 143. 6-.

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Abstract

We study a family of transcendental entire functions of genus zero, for which all of the zeros lie within a closed sector strictly smaller than a half-plane. In general these functions lie outside the Eremenko-Lyubich class. We show that for functions in this family the fast escaping set has Hausdorff dimension equal to two.

Item Type: Article
Uncontrolled Keywords: math.CV, math.CV, math.DS
Depositing User: Symplectic Admin
Date Deposited: 07 Apr 2017 08:34
Last Modified: 19 Jan 2023 07:06
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URI: https://livrepository.liverpool.ac.uk/id/eprint/3006834
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